Minibatch decomposition methods for empirical risk minimization are commonly analysed in a stochastic approximation setting, also known as sampling with replacement. On the other hands modern implementations of such techniques are incremental: they rely on sampling without replacement, for which available analysis are much scarcer. We provide convergence guaranties for the latter variant by analysing a versatile incremental gradient scheme. For this scheme, we consider constant, decreasing or adaptive step sizes. In the smooth setting we obtain explicit complexity estimates in terms of epoch counter. In the nonsmooth setting we prove that the sequence is attracted by solutions of optimality conditions of the problem.

翻译：尽量减少风险的经验性微小分解方法通常在随机近似环境中分析,也称为抽样和替换。在其他手方面,现代技术的采用是渐进的:它们依靠抽样而不替换,而现有的分析则少得多。我们通过分析多用途递增梯度办法,为后一种变式提供趋同保证。对于这一办法,我们考虑的是不变、递减或适应性梯度大小。在平稳的环境下,我们从环球计数中获得明确的复杂估计值。在非悬浮环境中,我们证明问题的最佳性条件的解决办法吸引了顺序。